Permeability is one of the key parameters in determining oil well productivity and optimizing reservoir management. Conventional techniques such as core sample evaluation in the lab or intermittent-sampling formation testing tools are slow and expensive. These methods are also impractical for providing a continuous permeability profile as a function of depth. Furthermore lab measurements of core samples in the lab can be inaccurate due to core damage. Measurement of permeability from acoustic data is one method of circumventing these difficulties, and numerous patents describing methods of estimating permeability from Stoneley waves have been published over the last several decades. All of these methods rely on the fact that Stoneley waves are attenuated and slowdown in permeable formations relative to impermeable ones due to slow P-wave coupling, and this effect can be quantified via a full or simplified Biot-Rosenbaum theory using specified boundary conditions, as noted in various articles.
Unfortunately, measurement of permeability from Stoneley wave data suffers from its own difficulties. As early as 1987, permeability was estimated from Stoneley wave slowness. See, for example, U.S. Pat. No. 4,797,859. However, the effect of low permeabilities on slowness is generally very small and easily obscured by uncertainties in other parameters. See, for example, X. M. Tang, A. Cheng, “Quantitative Borehole Acoustic Methods”, Handbook of Geophysical Exploration: Seismic Exploration, pp. 109-155, Vol. 24, 2004. It has been reported that Stoneley wave velocity is least sensitive to permeability. In order of importance, it has also been reported that Stoneley wave velocity is more sensitive to borehole mud velocity, shear velocity, and borehole size, and is least sensitive to permeability. See, for example, U.S. Pat. No. 7,830,744. Conversely, the Stoneley wave attenuation, as measured by inverse quality factor, is most sensitive to permeability. However, attenuation due to permeability can be masked by intrinsic attenuation and reflections due to borehole irregularities and formation heterogeneity. See, for example, X. M. Tang, A. Cheng, “Quantitative Borehole Acoustic Methods”, Handbook of Geophysical Exploration: Seismic Exploration, pp. 109-155, Vol. 24, 2004. Intrinsic attenuation is attenuation of the rock matrix that is not due to permeability. Several methods have been developed over the years attempting to address these issues.
A Biot model using an elastic membrane impedance model to account for mud cake has been developed, but did not consider intrinsic attenuation or reflections. See U.S. Pat. No. 4,964,101. Based on a modified version of U.S. Pat. No. 4,964,101, corrections for reflections have been considered by windowing the Stoneley wave based on its approximate arrival time. See U.S. Pat. No. 5,687,138. However this may not eliminate nearby reflections overlapping the direct Stoneley arrival. Velocity and intrinsic attenuation of the borehole fluid (but not of the formation) were determined by inversion over an impermeable region of the well. No correction was made for intrinsic attenuation of the formation. Corrections for reflections have been considered by using various two-mode frequency semblance methods, which did not consider the effect of intrinsic attenuation. See U.S. Pat. No. 5,331,604. Corrections for intrinsic attenuation have been considered using an empirical shale relationship and measurement of mud attenuation in a non-permeable clean sand. See U.S. Pat. No. 7,830,744 in which handling of reflections by time-frequency filtering and wave separation, if necessary, is suggested without providing details.
In U.S. Pat. No. 5,784,333, wave separation and synthetic one-dimensional (1-D) modeling of the corresponding effective elastic formation are used to correct for reflections, and a two-dimensional (2-D) inversion over permeability and intrinsic attenuation uses a simplified Biot model. This inversion requires knowledge of the transmitter-receiver response function, and uses an estimate of transmitter-receiver response at a depth of low or known permeability. The inversion estimates attenuation across the entire aperture from transmitter to receiver. A finer depth resolution is achieved in post processing by estimating the attenuation only across the receiver array. However, errors may exist in the estimate of the transmitter-to-receiver response functions used, which may affect the attenuation measurement.